Sabine Equation

The fundamental equation relating reverberation time to room volume and total absorption.

The Sabine equation, developed by Wallace Clement Sabine in the late 1890s, was the first mathematical formula for predicting reverberation time. It remains the foundation of architectural acoustics.

The equation states that reverberation time is proportional to room volume and inversely proportional to total absorption. This makes intuitive sense: larger rooms take longer to decay, and more absorption speeds up the decay.

The constant 0.161 (or 0.049 in imperial units) was determined empirically by Sabine through extensive measurements. It accounts for the speed of sound and the statistical nature of sound decay.

Limitations of the Sabine equation: • Assumes uniform absorption distribution (often not true) • Less accurate for highly absorptive rooms (Eyring equation better) • Assumes diffuse sound field (problematic in small rooms) • Ignores air absorption (significant at high frequencies in large rooms)

Despite these limitations, the Sabine equation remains essential for initial acoustic design calculations and understanding the relationships between room parameters.

Formula

RT60 = 0.161 × V / A

RT60 = Reverberation Time (seconds)
0.161 = Sabine Constant (s/m (metric))
V = Room Volume (m³)
A = Total Absorption (Sabins (m²))

Practical Example

Target RT60 = 0.4s in a 100 m³ room

A = 0.161 × 100 / 0.4 = 40.25 Sabins needed

You need 40 Sabins of absorption. If walls average α = 0.1 (about 14 Sabins), you need ~26 Sabins from treatment.

Standards: ISO 3382-1, ISO 3382-2

Related Terms

RT60 · Absorption Coefficient

Glossaire · Concepteur de Diffuseurs

ResonAia is an interactive acoustic design application. Enable JavaScript for the full experience, or follow the links above to explore the platform.